Einstein's kinetic theory of the Brownian motion, based upon light
water molecules continuously bombarding the heavy pollen, provided an explanation of diffusion from the Newtonian mechanics. Since the discovery of quantum mechanics it has been a challenge to verify the emergence of diffusion from the Schrodinger equation. In this talk I will report on a mathematically rigorous derivation of a diffusion equation
as a long time scaling limit of a random Schr\"odinger equation in a weak, uncorrelated disorder potential. This is a joint work with M. Salmhofer and H.T. Yau.